%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT033+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:56:04 AM UTC 2026
% Result : Theorem 1.91s 0.67s
% Output : CNFRefutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 10 unt; 0 def)
% Number of atoms : 70 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 68 ( 25 ~; 22 |; 11 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 1 sgn 11 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity_r1_tarski,axiom,
! [A,B] : r1_tarski(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(fc5_ens_1,axiom,
! [A] :
( ( l1_cat_1(A)
& v2_cat_1(A) )
=> ~ v1_xboole_0(k17_ens_1(A)) ),
file('theBenchmark.p',fc5_ens_1) ).
fof(d1_yoneda_1,axiom,
! [A] :
( ( l1_cat_1(A)
& v2_cat_1(A) )
=> k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A)) ),
file('theBenchmark.p',d1_yoneda_1) ).
fof(t49_ens_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( l1_cat_1(B)
& v2_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_cat_1(B))
=> ( r1_tarski(k17_ens_1(B),A)
=> m2_cat_1(k20_ens_1(B,C),B,k12_ens_1(A)) ) ) ) ),
file('theBenchmark.p',t49_ens_1) ).
fof(t2_yoneda_1,conjecture,
! [A] :
( ( l1_cat_1(A)
& v2_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> m2_cat_1(k20_ens_1(A,B),A,k1_yoneda_1(A)) ) ),
file('theBenchmark.p',t2_yoneda_1) ).
fof(t2_yoneda_1_neg,negated_conjecture,
~ ! [A] :
( ( l1_cat_1(A)
& v2_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> m2_cat_1(k20_ens_1(A,B),A,k1_yoneda_1(A)) ) ),
inference(assume_negation,[status(cth)],[t2_yoneda_1]) ).
cnf(c_113,plain,
r1_tarski(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_127,plain,
( ~ v1_xboole_0(k17_ens_1(A))
| ~ l1_cat_1(A)
| ~ v2_cat_1(A) ),
inference(clausify,[status(thm)],[fc5_ens_1]) ).
cnf(c_135,plain,
( k12_ens_1(k17_ens_1(A)) = k1_yoneda_1(A)
| ~ l1_cat_1(A)
| ~ v2_cat_1(A) ),
inference(clausify,[status(thm)],[d1_yoneda_1]) ).
cnf(c_136,plain,
( m2_cat_1(k20_ens_1(B,C),B,k12_ens_1(A))
| ~ r1_tarski(k17_ens_1(B),A)
| ~ m1_subset_1(C,u1_cat_1(B))
| ~ l1_cat_1(B)
| ~ v2_cat_1(B)
| v1_xboole_0(A) ),
inference(clausify,[status(thm)],[t49_ens_1]) ).
fof(nnf_52,plain,
? [A] :
( ? [B] :
( ~ m2_cat_1(k20_ens_1(A,B),A,k1_yoneda_1(A))
& m1_subset_1(B,u1_cat_1(A)) )
& l1_cat_1(A)
& v2_cat_1(A) ),
inference(fof_nnf,[status(thm)],[t2_yoneda_1_neg]) ).
fof(sk_t2_yoneda_1_neg,plain,
( ~ m2_cat_1(k20_ens_1(sK0,sK1),sK0,k1_yoneda_1(sK0))
& m1_subset_1(sK1,u1_cat_1(sK0))
& l1_cat_1(sK0)
& v2_cat_1(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_52]) ).
cnf(c_137,negated_conjecture,
v2_cat_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t2_yoneda_1_neg]) ).
cnf(c_138,negated_conjecture,
l1_cat_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t2_yoneda_1_neg]) ).
cnf(c_139,negated_conjecture,
m1_subset_1(sK1,u1_cat_1(sK0)),
inference(split_conjunct,[status(thm)],[sk_t2_yoneda_1_neg]) ).
cnf(c_140,negated_conjecture,
~ m2_cat_1(k20_ens_1(sK0,sK1),sK0,k1_yoneda_1(sK0)),
inference(split_conjunct,[status(thm)],[sk_t2_yoneda_1_neg]) ).
cnf(c_513,negated_conjecture,
( k12_ens_1(k17_ens_1(sK0)) = k1_yoneda_1(sK0)
| ~ l1_cat_1(sK0) ),
inference(resolve,[status(thm)],[c_137,c_135]) ).
cnf(c_476,negated_conjecture,
k12_ens_1(k17_ens_1(sK0)) = k1_yoneda_1(sK0),
inference(resolve,[status(thm)],[c_138,c_513]) ).
cnf(c_514,negated_conjecture,
( ~ v1_xboole_0(k17_ens_1(sK0))
| ~ l1_cat_1(sK0) ),
inference(resolve,[status(thm)],[c_137,c_127]) ).
cnf(c_477,negated_conjecture,
~ v1_xboole_0(k17_ens_1(sK0)),
inference(resolve,[status(thm)],[c_138,c_514]) ).
cnf(c_515,negated_conjecture,
( m2_cat_1(k20_ens_1(sK0,B),sK0,k12_ens_1(A))
| ~ r1_tarski(k17_ens_1(sK0),A)
| ~ m1_subset_1(B,u1_cat_1(sK0))
| ~ l1_cat_1(sK0)
| v1_xboole_0(A) ),
inference(resolve,[status(thm)],[c_136,c_137]) ).
cnf(c_516,negated_conjecture,
( m2_cat_1(k20_ens_1(sK0,B),sK0,k12_ens_1(A))
| ~ r1_tarski(k17_ens_1(sK0),A)
| ~ m1_subset_1(B,u1_cat_1(sK0))
| v1_xboole_0(A) ),
inference(resolve,[status(thm)],[c_515,c_138]) ).
cnf(c_517,negated_conjecture,
( m2_cat_1(k20_ens_1(sK0,sK1),sK0,k12_ens_1(A))
| ~ r1_tarski(k17_ens_1(sK0),A)
| v1_xboole_0(A) ),
inference(resolve,[status(thm)],[c_516,c_139]) ).
cnf(c_518,negated_conjecture,
( m2_cat_1(k20_ens_1(sK0,sK1),sK0,k12_ens_1(k17_ens_1(sK0)))
| v1_xboole_0(k17_ens_1(sK0)) ),
inference(resolve,[status(thm)],[c_517,c_113]) ).
cnf(c_519,negated_conjecture,
( m2_cat_1(k20_ens_1(sK0,sK1),sK0,k1_yoneda_1(sK0))
| v1_xboole_0(k17_ens_1(sK0)) ),
inference(paramod,[status(thm)],[c_476,c_518]) ).
cnf(c_520,negated_conjecture,
m2_cat_1(k20_ens_1(sK0,sK1),sK0,k1_yoneda_1(sK0)),
inference(resolve,[status(thm)],[c_477,c_519]) ).
cnf(c_512,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_140,c_520]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT033+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 22:59:04 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2727560 was started by sandbox2 on n020,
% 0.09/0.37 % Sat Sep 26 22:59:04 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.38
% 0.13/0.38 % From the command line: assign(max_seconds, 300).
% 1.91/0.67
% 1.91/0.67 % SZS status Theorem for theBenchmark
% 1.91/0.67
% 1.91/0.67 % Proof 1 at 0.27 (+ 0.01) seconds.
% 1.91/0.67 % Length of proof is 16.
% 1.91/0.67 % Level of proof is 3.
% 1.91/0.67 % Maximum clause weight is 31.000.
% 1.91/0.67 % Given clauses 69.
% 1.91/0.67
% 1.91/0.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------